The Gunners fell behind when Claudio Yacob headed home Morgan Amalfitano's rightwing cross in the 42nd minute at The Hawthorns before Jack Wilshere fired home a deflected 20-yard effort not long after the hour-mark.
After the match, Wenger believed the draw was the proper result after both sides missed gilt-edged chances to sew up the contest.
"Over the whole game, I think it's a fair point. Over the last half-an-hour, I have some regrets, because we could feel we had the opportunities to score a second goal," he told Sky Sports 1.
"We again have shown character to come back into this game and in the second half being a goal down to equalise."
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